tools: replace custom new-with-error rule

Use no-restricted-syntax to implement the requirement that `Error`
objects must be thrown with the `new` keyword.

PR-URL: #12249
Reviewed-By: James M Snell <jasnell@gmail.com>
Reviewed-By: Richard Lau <riclau@uk.ibm.com>
Reviewed-By: Colin Ihrig <cjihrig@gmail.com>
Reviewed-By: Teddy Katz <teddy.katz@gmail.com>
Reviewed-By: Gibson Fahnestock <gibfahn@gmail.com>

Author: Trott